The paper attempts to assess the effectiveness of software testing performed based on a tests set constructed using random methods. General rules that should be taken into account in the process of preparing a tests set for program testing are described. On the basis of a formal description of the testing process the methods of determining the size of the set of tests are discussed. The cardinality of the tests set constituting the basis for the program testing process is proposed to be determined as a result of solving the formal two-criteria optimization problem. Received solution to such problem allows both maximization of the probability of covering all executable paths of the tested program and minimizing the cost of the testing process implementation. The presented considerations are illustrated with a numerical example.